Fourier Transform of Cosine Function with Step Function Constraints

[electron2]

<br /> f(t-a)u_a(t)-&gt;F(s)e^{-as}<br />
<br /> g(t)={\cos (t),0&lt;=t&lt;\pi}<br />
<br /> g(t)={0,t&gt;=\pi}<br />

<br /> g(t)=\cos(t)[ u(t)-u(t-\pi)]=\cos(t) u(t)-\cos(t) u(t-\pi)=\frac{s}{s^2-1}+??\\<br />

i can't apply the formula in the last part

 

[HallsofIvy]

Trig formula cos(t-\pi)= -cos(t).

 

[electron2]

g(t)=\cos(t)[ u(t)-u(t-\pi)]=\cos(t) u(t)+\cos(t-\pi) u(t-\pi)=\frac{s}{s^2-1}+\frac{s}{s^2-1}e^{-\pi}\\

is it correct?